lec93-ポアソン分布.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "昼のピーク時にお客様が7人である確率は、9.01%です\n"
     ]
    }
   ],
   "source": [
    "# 期待値λは10\n",
    "lamb = 10\n",
    "\n",
    "# ちょうど7人来る確率を計算する\n",
    "k = 7\n",
    "\n",
    "from math import exp\n",
    "from math import factorial\n",
    "\n",
    "# 確率質量関数を使って確率を計算する\n",
    "prob = (lamb**k)*exp(-lamb)/factorial(k)\n",
    "\n",
    "print(f'昼のピーク時にお客様が7人である確率は、{100*prob:0.2f}%です')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ピーク時に7人の確率は9.01%\n",
      "平均=10.0\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import poisson\n",
    "\n",
    "mu = 10\n",
    "\n",
    "mean,var = poisson.stats(mu)\n",
    "\n",
    "odds_seven = poisson.pmf(7,mu)\n",
    "\n",
    "print(f'ピーク時に7人の確率は{odds_seven*100:0.2f}%')\n",
    "print(f'平均={mean}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4.53999298e-05, 4.53999298e-04, 2.26999649e-03, 7.56665496e-03,\n",
       "       1.89166374e-02, 3.78332748e-02, 6.30554580e-02, 9.00792257e-02,\n",
       "       1.12599032e-01, 1.25110036e-01, 1.25110036e-01, 1.13736396e-01,\n",
       "       9.47803301e-02, 7.29079462e-02, 5.20771044e-02, 3.47180696e-02,\n",
       "       2.16987935e-02, 1.27639962e-02, 7.09110899e-03, 3.73216263e-03,\n",
       "       1.86608131e-03, 8.88610150e-04, 4.03913704e-04, 1.75614654e-04,\n",
       "       7.31727725e-05, 2.92691090e-05, 1.12573496e-05, 4.16938875e-06,\n",
       "       1.48906741e-06, 5.13471521e-07])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 確率質量関数をプロットする\n",
    "import numpy as np\n",
    "\n",
    "# 30人お客様が来る確率\n",
    "k = np.arange(30)\n",
    "\n",
    "# 平均は10\n",
    "lamb = 10\n",
    "\n",
    "pmf_pois = poisson.pmf(k,lamb)\n",
    "pmf_pois"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 30 artists>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline\n",
    "\n",
    "plt.bar(k,pmf_pois)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "10人より多くお客様が来る確率を求める"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "お客様が10人までの確率は、58.30%です\n"
     ]
    }
   ],
   "source": [
    "# お客様が10人までの確率を計算するので、k = 10、平均値 = 10\n",
    "k,mu = 10,10\n",
    "\n",
    "# お客様が10人までの確率を計算する\n",
    "prob_up_to_ten = poisson.cdf(k,mu)\n",
    "\n",
    "print(f'お客様が10人までの確率は、{100*prob_up_to_ten:0.2f}%です')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "10人より多く来る確率は、1からこの値を引くだけ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10人より多くのお客様が来る確率は、41.70%です\n"
     ]
    }
   ],
   "source": [
    "prob_more_than_ten = 1 - prob_up_to_ten\n",
    "\n",
    "print(f'10人より多くのお客様が来る確率は、{prob_more_than_ten*100:0.2f}%です')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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